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In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline by using trigonometry, rather than measuring distances to the point directly as in trilateration. The point can then be fixed as the third point of a triangle with one known side ...
Measuring the height of a building with an inclinometer. Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and, in the military, the gun direction, the trajectory and distribution of fire power of weapons. The use of triangles to estimate distances dates to ...
Heron's formula. A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths Letting be the semiperimeter of the triangle, the area is [1] It is named after first-century engineer Heron of Alexandria (or Hero) who ...
The extended sides of the orthic triangle meet the opposite extended sides of its reference triangle at three collinear points. [22] [23] [21] In any acute triangle, the inscribed triangle with the smallest perimeter is the orthic triangle. [24] This is the solution to Fagnano's problem, posed in 1775. [25]
In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular ...
In computer graphics, a triangulated irregular network (TIN) [1] is a representation of a continuous surface consisting entirely of triangular facets (a triangle mesh), used mainly as Discrete Global Grid in primary elevation modeling. The vertices of these triangles are created from field recorded spot elevations through a variety of means ...
Shoelace formula. The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2] It is called the shoelace formula because of the constant cross-multiplying for the ...
A triangulation station, also known as a trigonometrical point, and sometimes informally as a trig, is a fixed surveying station, used in geodetic surveying and other surveying projects in its vicinity. The nomenclature varies regionally: they are generally known as trigonometrical stations or triangulation stations in North America, trig ...